How is D related to A? Statement I: B is the brother of A. Statement II: B is the son of D.

Introduction / Context:
This data sufficiency question tests understanding of family relationships and the limits of information provided by two short statements. The task is to determine how D is related to A, that is, whether D is a parent, grandparent, uncle, or has some other fixed relation, based only on the information in the two statements. The key idea is to check whether any single statement or the combination of both statements forces one unique relation between D and A, without allowing alternative possibilities that are still consistent with the given data.

Given Data / Assumptions:

• Statement I: B is the brother of A.
• Statement II: B is the son of D.
• Family relationships are assumed to be in the usual sense, with brother meaning a male sibling.
• No extra information about parents, step relations, or half siblings is given.
• We must identify the relation of D to A in a unique and definite way.

Concept / Approach:
The standard approach in data sufficiency is:

• First, analyse statement I alone and see whether it is enough.
• Next, analyse statement II alone.
• Then, combine both statements to check whether together they yield a unique answer.
• If even the combination does not lead to a single fixed relation, the data are considered insufficient.

Here, the core concept is that if multiple different family structures fit the statements, then the relation of D to A cannot be uniquely determined.

Step-by-Step Solution:
Step 1: From statement I, B is the brother of A. So A and B share at least one common parent, but we are told nothing about D. Step 2: From statement I alone, D is never mentioned, so statement I alone is clearly not sufficient to decide the relation of D to A. Step 3: From statement II, B is the son of D. So D is a parent of B, but there is no mention of A. Step 4: From statement II alone, we know B is a child of D, but we do not know whether A is also a child of D, a child of only one parent common with B, or only a step or half sibling. Step 5: Now combine both statements. We know B is the brother of A, and B is the son of D. This means that B is a male child of D and that A is a sibling of B. Step 6: However, A could be a full child of D, a stepchild, or a child of a different parent who is married to D. All these cases still satisfy both statements. Step 7: Because there are multiple possibilities, D may be the father or mother of A, or possibly a step parent. No unique relation can be fixed.

Verification / Alternative check:
Alternative scenario 1: Suppose A is also a child of D. Then D is a parent of A. Alternative scenario 2: Suppose A is the child of the other parent only, and B is the only child of D with that partner. Then A is still a sibling of B, but D is a step parent to A, not a biological parent. Both scenarios satisfy statement I and statement II, yet the relation of D to A is not the same. This confirms that the relation is not uniquely determined even when both statements are used together.

Why Other Options Are Wrong:
Option a is wrong because statement I does not mention D at all. Option b is wrong because statement II only tells us about B and D, not about A. Option c is wrong because neither statement alone can ever be enough, so it is impossible that either alone is sufficient. Option d is wrong because even with both statements, multiple family configurations are possible, so the relation is not uniquely fixed.

Common Pitfalls:
Many students quickly assume that if B is the brother of A and B is the son of D, then A must also be the child of D, so D is a parent of A. This assumes that all siblings share both parents, which is not guaranteed by the statements. The question does not exclude step siblings or half siblings. In data sufficiency problems, one must avoid adding hidden assumptions. Unless the question clearly states that all siblings are born to the same parents, you must allow more than one logically possible family structure. As soon as more than one family structure fits the data, the information is not sufficient to give a unique answer about the required relation.

Final Answer:
Even using both statements I and II together, the relation of D to A cannot be uniquely determined, so the data are not sufficient. Correct option: Even using both statements I and II together, the data are not sufficient to answer the question.